13.9.4 problem 4

Internal problem ID [2390]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 4
Date solved : Monday, January 27, 2025 at 05:51:21 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 11

dsolve([4*diff(y(t),t$2)-4*diff(y(t),t)+y(t)=0,y(0) = 0, D(y)(0) = 3],y(t), singsol=all)
 

\[ y = 3 t \,{\mathrm e}^{\frac {t}{2}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 15

DSolve[{4*D[y[t],{t,2}]-4*D[y[t],t]+y[t]==0,{y[0]==0,Derivative[1][y][0] ==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 3 e^{t/2} t \]